A Point-Symmetric Graph that is Nowhere Reversible
Frank Harary, Andrew Vince, Dale Worley · SIAM Journal on Algebraic and Discrete Methods · 1982
It is the purpose of this note to investigate the relationships among four concepts relating to symmetry in graphs: point-symmetry, line-symmetry, arc-symmetry and reversibility; especially which of the first three properties do not imply reversibility. Holt has found a counterexample to one such question and we construct a counterexample to another using a Cayley graph. Both examples are nowhere reversible, a property which is stronger than nonreversibility.